Hugelkultur is a method of burying wood to compost it. If you cannot bury down, then bury up. That is, put the wood on the bottom, pile other organic material on top, then add a thin layer of soil or potting medium in which to plant things. Twigs, brush, or even whole logs all work for this. Hugelkultur includes a vertical model as well as a horizontal one.
Another method you may like is the lasagna garden. You can make the bottom layer out of brush for ventilation and water retention if you pile the upper layers deep enough. Alternatively you can run your brush through a wood chipper and use the chips, which are small enough to compost easily.
If you want to use soil production and enrichment methods, then I strongly recommend that you study soil formation and the denizens of the detritus food chain. You do not need to get into the advanced science, unless you just want to because it's fun. You just need to know basically how this stuff happens naturally, so you can help it along and not fuck it up. Here at Fieldhaven, my detritus food chain is 3 days to apex. Literally, one time we had a fallen tree chipped up, it rained for three days, and when I could finally get out to examine the pile of chips, it already had fungal webs and when I stuck a trowel into it a toad crawled out. If you make a congenial habitat, the wildlife will come.
You can also work with your local habitat to encourage native species. Look for small cups or cracks in the rock. Fill those with soil similar to the surroundings. Plant native wildflowers there. If you don't want to spend money, just gather seeds from whatever pretty plants grow in your area and cram those into the dirt pockets instead. It's possible to turn a rock face into a rather spectacular garden this way. All you're really doing is speeding up the natural processes a bit.
For this, use techniques from rock gardening, except you get to skip the tedious process of making the rock garden.
Stone Walls and Plants That Grow in Them
Drought-Smart Plants for Rock Gardens
If you can't reach some of the areas where you would like to plant wildflowers, then make seed bombs and heave them up there. Use a slingshot or catapult for extra loft. The seed bombs will catch in cracks or cups high up the rock face and, eventually, sprout.
Terracing works too. This involves making walls to create a series of flat gardening surfaces that move in small steps down the slope.
There are also general tips on mountain gardening.
As a rule, anything that grows in a mountainous area is likely to grow on your particular mountain, but native species have the highest chance of success and the most wildlife value. Try to decorate with natives and reserve exotics for things you want to eat or use that don't really have native equivalents.